Your going to get your normal crowd who will tell you that you can tow anything with a 1500 and the crowd that will tell you your negligent. Neither can tell you what YOU can or cannot do, that's up to you.
I would tackle a 4000pd camper with your truck! Would I want to do it for 20000 miles a year, not really but if I was not in any hurry, say retired would consider it. Main thing for me is how long will the truck last? It is the better part of 13 years old, yes 70k on it but it is still 13years old. I am not overly mechanical and would need to rely on shops to fix it if something happened, towing a lot with it I would expect some issues to pop up.
Tranny cooler if not already installed is a must in my opinion, cheap and relatively easy to add.
I will advise you to pay attention to your weights, i think they were put on the truck for more then just Chevs peace of mind. Personally I have found that when I get past 80% of the recommended tow rating the tow vehical handles poorly. Only can comment on a travel trailer and that experiance though, my fifth wheel is hauled by a DRW truck that's not close to its tow rating.